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The speed v at which a rigid sphere falls through a viscous fluid depends on the difference in density between the sphere and the fluid, Ap, the radius of the sphere, a, and the viscosity of the fluid, 7, and is given by 2 gApa? 9 where g is the acceleration due to gravity. (a) East Coast beaches are dominated by quartz sand. A medium-sized grain of sand has a radius of 0.5 mm. The density of quartz is 2.65 g/cc (2650 kg/m³); the density of water is about 1 g/cc (1000 kg/m³). The viscosity of water at 20°C is 10-3 Pa s. The acceleration due to gravity is about 9.81 m/s2. How long will it take for the grain of sand to sink through 10 m of water?

The speed v at which a rigid sphere falls through a viscous fluid depends on the difference in density between the sphere and the fluid, Ap, the radius of the sphere, a, and the viscosity of the fluid, 7, and is given by 2 gApa? 9 where g is the acceleration due to gravity. (a) East Coast beaches are dominated by quartz sand. A medium-sized grain of sand has a radius of 0.5 mm. The density of quartz is 2.65 g/cc (2650 kg/m³); the density of water is about 1 g/cc (1000 kg/m³). The viscosity of water at 20°C is 10-3 Pa s. The acceleration due to gravity is about 9.81 m/s2. How long will it take for the grain of sand to sink through 10 m of water?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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The speed v at which a rigid sphere falls through a viscous fluid depends on the difference in density between the sphere and the fluid, Ap, the radius of the sphere, a, and the viscosity of the fluid, 7, and is given by 2 gApa? v = 9 where q is the acceleration due to gravity. (a) East Coast beaches are dominated by quartz sand. A medium-sized grain of sand has a radius of 0.5 mm. The density of quartz is 2.65 g/cc (2650 kg/m³); the density of water is about 1 g/cc (1000 kg/m³). The viscosity of water at 20°C is 10-3 Pa s. The acceleration due to gravity is about 9.81 m/s². How long will it take for the grain of sand to sink through 10 m of water? (b) How fast does a sphere of radius 1 cm fall compared to a sphere of radius 0.5 mm in the same fluid? (c) Where a stream enters a pond, it is often observed that coarser sediment such as gravel is deposited near the mouth of the stream, while finer sediments such as sand and silt are deposited farther into the pond. Explain this observation.
Transcribed Image Text:The speed v at which a rigid sphere falls through a viscous fluid depends on the difference in density between the sphere and the fluid, Ap, the radius of the sphere, a, and the viscosity of the fluid, 7, and is given by 2 gApa? v = 9 where q is the acceleration due to gravity. (a) East Coast beaches are dominated by quartz sand. A medium-sized grain of sand has a radius of 0.5 mm. The density of quartz is 2.65 g/cc (2650 kg/m³); the density of water is about 1 g/cc (1000 kg/m³). The viscosity of water at 20°C is 10-3 Pa s. The acceleration due to gravity is about 9.81 m/s². How long will it take for the grain of sand to sink through 10 m of water? (b) How fast does a sphere of radius 1 cm fall compared to a sphere of radius 0.5 mm in the same fluid? (c) Where a stream enters a pond, it is often observed that coarser sediment such as gravel is deposited near the mouth of the stream, while finer sediments such as sand and silt are deposited farther into the pond. Explain this observation.
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